STABILITY ANALYSIS FOR LINEAR NON-AUTONOMOUS SYSTEMS WITH CONTINUOUSLY DISTRIBUTED MULTIPLE TIME-VARYING DELAYS AND … (original) (raw)

Stability Analysis of Linear Systems with Time Delays

This paper addresses exponential stability problem for a class of linear systems with time delay. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, new sufficient conditions for the exponential stability of the systems are first established in terms of LMIs.

Exponential Stability of Linear Systems with Multiple Time Delays

Mathematical Researches, 2016

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new system, by using matrix decomposition and linear matrix inequality (LMI) technique. Some numerical examples are given to illustrate the efficiency of our method.

Novel Results for Global Exponential Stability of Uncertain Systems with Interval Time-varying Delay

This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

Exponential stability and stabilization of a class of uncertain linear time-delay systems

Journal of the Franklin Institute, 2009

This paper provide exponential stability conditions for a class of uncertain linear hybrid time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also timevarying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. An application to stabilization of linear control switching systems is given. Numerical examples are given to illustrate the results.

Improved delay-dependent exponential stability criteria for time-delay system

Journal of the Franklin Institute, 2013

This paper considers the problem of time delay-dependent exponential stability criteria for the time-delay linear system. Utilizing the linear inequality matrices (LMIs) and slack matrices, a novel criterion based on the Lyapunov-Krasovskii methodology is derived for the exponential stability of the time-delay system. Based on the criteria condition we concluded that the upper bound of the exponential decay rate for the time-delay system can be easily calculated. In addition, an improved sufficient condition for the robust exponential stability of uncertain time-delay system is also proposed. Numerical examples are provided to show the effectiveness of our results. Comparisons between the results derived by our criteria and the one given in Liu (2004) [1], Mondie and Kharitonov (2005) [2], and Xu et al. (2006) [3] show that our methods are less conservative in general. Furthermore, numerical results also show that our criteria can guarantee larger exponential decay rates than the ones derived by Liu (2004) [1] and Mondie and Kharitonov (2005) [2] in all time delay points we have tested and in some of time delay points obtained by Xu et al. (2006) [3].

An improved criterion for exponential stability of linear systems with multiple time delays

Applied Mathematics and Computation, 2008

Exponential stability of linear systems with multiple time delays is studied in this paper. By using an improved Lyapunov functional, we have obtained an improved criterion, which is strictly less conservative than the very recent criterion in Ren and Cao [Fengli Ren, Jinde Cao, Novel a-stability of linear systems with multiple time delays, Appl. Math. Comput. 181 (2006), 282-290], and an estimation of Lyapunov factor. A numerical example is also given to shown the superiority of our result to those in the literature.

New Criteria for Exponential Stability of Linear Time-Varying Differential Systems with Delay

Taiwanese Journal of Mathematics, 2014

General linear time-varying differential systems with delay are considered. Several explicit criteria for exponential stability are presented. Furthermore, an explicit robust stability bound for systems subject to time-varying perturbations is given. Two examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.

Delay-dependent stability analysis of linear systems with time-varying delay

2007 46th IEEE Conference on Decision and Control, 2007

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay dependent stability conditions are then formulated in terms of linear matrix inequalities (LMI). Finally, an example shows the effectiveness of the proposed methodology.